What browser version are you using?
Currently, Firefox 31.0, under 64-bit Windows 7. I also have 32-bit Firefox on Xubuntu 12.04 and XP Pro, but I haven't logged into eham.com lately using those, because I wanted to eliminate the possibility that the problems might have been caused by accessing eHam with two different machines. But it's happened on those machines before, also.
I don't think eHam uses Java. For well over a year, Java has been disabled here for well-known recurring security reasons.
The thing is, sometimes it all works. A few weeks ago, it seemed that if I waited 5 or 10 seconds between each step: logging out to delete the cookies, logging back in, checking for new messages, and marking all messages read, it helped. The errors occurred much less often. But one day, doing that didn't work anymore.
In the past month or so, logging out and back in usually --but not always-- lets me mark all messages read (doing so did not help until recently). Even when that works, I sometimes get an error message when trying to reply or enable notifications that can only be fixed by deleting all eHam cookies when logged out. I've tried many things including changing the sequences of the steps.
This ongoing problem is unbelievably frustrating. I've wanted to explain all this for some time, but I held back because I'm not a big contributor of funds to this site.